Discussion

Explanation:

Let P = (1 – x² + x³)(1 + x)¹⁰

The terms containing x⁷, x⁵ and x⁴ in the expansion of (1 + x)¹⁰ give terms containing x⁷ in the expression of P.

The r^th term in the Binomial Expansion of (a + b)ⁿ is given by

T_r = ⁿC_r – 1 a^{(n – r – 1)}b^{(r – 1)}

∴ The term containing x⁷ is given by

T₈ = ¹⁰C₇ x⁷

The term containing x⁵ is given by

T₆ = ¹⁰C₅x⁵

The term containing x⁴ is given by

T₅ = ¹⁰C₄x⁴

∴ P = (1 – x² + x³)(¹⁰C₇ x⁷ + … + ¹⁰C₅x⁵ + ¹⁰C₄x⁴ + … )

∴ The coefficient of the term containing x⁷ = ¹⁰C₇ – ¹⁰C₅ + ¹⁰C₄

= 120 – 252 + 210 = 78

Hence, option (b).

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